A242672 Decimal expansion of an optimal stopping constant related to the Secretary problem.

3, 8, 6, 9, 5, 1, 9, 2, 4, 1, 3, 9, 7, 9, 9, 9, 4, 9, 5, 6, 9, 4, 1, 6, 7, 2, 7, 8, 7, 7, 9, 0, 8, 3, 4, 3, 2, 1, 9, 4, 6, 0, 6, 4, 3, 2, 5, 1, 9, 6, 9, 3, 3, 4, 4, 0, 4, 3, 9, 6, 0, 8, 9, 1, 1, 7, 0, 5, 9, 6, 2, 9, 9, 7, 8, 9, 8, 0, 3, 1, 5, 6, 0, 7, 0, 3, 6, 0, 6, 6, 7, 6, 1, 8, 4, 9, 3, 0, 8, 7, 1, 9, 7, 5, 7, 5

Offset

1,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.15, p. 362.

Links

Table of n, a(n) for n=1..106.

Eric Weisstein's MathWorld, Sultan's Dowry Problem.

Wikipedia, Secretary problem.

Formula

product_(k>0) (1+2/k)^(1/(k+1)).

Also equals exp(2*Sum_{k>=3} (log(k)/(k^2-1)) - log(2)/3).

Example

3.869519241397999495694167278779...

Mathematica

NProduct[(1+2/k)^(1/(k+1)), {k, 1, Infinity}, NProductFactors -> 1000, WorkingPrecision -> 48] // RealDigits[#, 10, 40]& // First

Crossrefs

Cf. A054404, A242673, A242674.

Sequence in context: A154199 A083700 A341747 * A021725 A371472 A295573

Adjacent sequences: A242669 A242670 A242671 * A242673 A242674 A242675

Keyword

nonn,cons

Author

Jean-François Alcover, May 20 2014

Extensions

More terms from Alois P. Heinz, Jun 06 2014

Status

approved